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	<title>Bag of Beans &#187; cosmology</title>
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		<title>The mystery of dark matter just refuses to be solved [Astrophysics]</title>
		<link>http://bagofbeans.tsangal.org/archives/7667</link>
		<comments>http://bagofbeans.tsangal.org/archives/7667#comments</comments>
		<pubDate>Mon, 17 Oct 2011 22:02:22 +0000</pubDate>
		<dc:creator>author-unknown</dc:creator>
				<category><![CDATA[syndicated]]></category>
		<category><![CDATA[Astronomy]]></category>
		<category><![CDATA[astrophysics]]></category>
		<category><![CDATA[Cold dark matter]]></category>
		<category><![CDATA[cosmology]]></category>
		<category><![CDATA[dark matter]]></category>
		<category><![CDATA[dwarf galaxy]]></category>
		<category><![CDATA[galaxy]]></category>
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		<category><![CDATA[Weakly interacting massive particle]]></category>
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		<description><![CDATA[Dark matter almost certainly exists - otherwise, galaxy clusters wouldn't have sufficient gravity to hold themselves together. It was hoped dwarf galaxies could confirm the leading dark matter theories. But a new study has drawn a big, frustrating blan... <a href="http://bagofbeans.tsangal.org/archives/7667">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p class="syndicated-attribution"><em>(via <a href="http://feeds.gawker.com/~r/io9/vip/~3/dAq6mjI8bSA/the-mystery-of-dark-matter-just-refuses-to-be-solved">io9</a>)</em></p>
<p><a rel="lytebox" href="http://cache.gawkerassets.com/assets/images/8/2011/10/darkmatter.jpg"><img src="http://cache.gawker.com/assets/images/io9/2011/10/darkmatter.jpg" width="500" alt="The mystery of dark matter just refuses to be solved" title="The mystery of dark matter just refuses to be solved"></a>Dark matter almost certainly exists - otherwise, galaxy clusters wouldn't have sufficient gravity to hold themselves together. It was hoped dwarf galaxies could confirm the leading dark matter theories. But a new study has drawn a big, frustrating blank. </p>
<p>Dwarf galaxies are considered ideal candidates to go dark matter hunting, because calculations suggest they're composed of up to 99% dark matter. The problem, of course, is that while we know there should be lots of dark matter there, we still don't really know exactly what dark matter <em>is</em>. In recent years, the most popular theory has been that super-heavy exotic particles are the key source of dark matter, and their relatively high subatomic mass means that they don't interact much with normal matter.</p>
<p>This is known as the cold dark matter model, and it suggests that sets of these particles clump together gravitationally, forming the cores of galaxies. Over time, normal matter is attracted to the dark matter and, from that, an entire galaxy is born. That suggests — and plenty of simulations and theoretical models have backed this up — that dark matter should be clustered at the centers of galaxies.</p>
<p>That's why a new study from the Harvard-Smithsonian Center for Astrophysics is such bad news. They examined the dark matter distributions of two dwarf galaxies and found that there was no higher concentration in the center of the galaxy than anywhere else. The dark matter was actually evenly distributed throughout the galaxy. The current cosmological model doesn't predict that, and it only adds to the challenge of figuring out just what is going on with dark matter.</p>
<p>Researcher Matt Walker, a Hubble Fellow at the Center for Astrophysics, explains why this result is so baffling:</p>
<blockquote>
<p>"After completing this study, we know less about dark matter than we did before. Our measurements contradict a basic prediction about the structure of cold dark matter in dwarf galaxies. Unless or until theorists can modify that prediction, cold dark matter is inconsistent with our observational data."</p>
</blockquote>
<p>University of Cambridge researcher Jorge Peñarrubia, who worked with Walker on the study, explains what they saw in the two dwarf galaxies:</p>
<blockquote>
<p>"Stars in a dwarf galaxy swarm like bees in a beehive instead of moving in nice, circular orbits like a spiral galaxy. That makes it much more challenging to determine the distribution of dark matter. If a dwarf galaxy were a peach, the standard cosmological model says we should find a dark matter 'pit' at the center. Instead, the first two dwarf galaxies we studied are like pitless peaches."</p>
</blockquote>
<p>So where do we go from here? Well, it definitely doesn't invalidate the basic dark matter model - as much as this is a less than encouraging result, dark matter still stands up to scrutiny far better than any of the alternatives, such as Modified Newtonian Dynamics (MOND) - if you don't believe me, check out Dr. Dave Goldberg's <a href="http://io9.com/5528758/ask-a-physicist-why-believe-in-dark-matter">fantastic primer on all things dark matter</a>. This may well mean that we need to move away from the cold dark matter model to other explanations, although only cold dark matter really explains the formation of galaxies.</p>
<p>This is all very much a mystery, and dark matter rather stubbornly refuses to reveal its secrets. The solution to all this is still anyone's guess, but hopefully further study can get us closer to, not further away from, what's actually going on.</p>
<p><em>Via the <a href="http://www.cfa.harvard.edu/news/2011/pr201129.html">Center for Astrophysics</a>. Artist's conception of dwarf galaxy by David A. Aguilar (CfA).</em></p><div>
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		<title>The Higgs boson might explain the origins of the universe and dark energy [Mad Science]</title>
		<link>http://bagofbeans.tsangal.org/archives/7125</link>
		<comments>http://bagofbeans.tsangal.org/archives/7125#comments</comments>
		<pubDate>Wed, 21 Sep 2011 22:49:47 +0000</pubDate>
		<dc:creator>author-unknown</dc:creator>
				<category><![CDATA[syndicated]]></category>
		<category><![CDATA[cosmology]]></category>
		<category><![CDATA[dark energy]]></category>
		<category><![CDATA[Dilaton]]></category>
		<category><![CDATA[Expansion]]></category>
		<category><![CDATA[Higgs boson]]></category>
		<category><![CDATA[Inflation]]></category>
		<category><![CDATA[mad science]]></category>
		<category><![CDATA[Physics]]></category>
		<category><![CDATA[science]]></category>
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		<category><![CDATA[Universe]]></category>

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		<description><![CDATA[We still haven't found the Higgs boson, the hypothetical particle that explains why other particles possess mass. But that might not be the only cosmic mystery the Higgs can solve. It could also explain how the universe got its shape. 
That's the theor... <a href="http://bagofbeans.tsangal.org/archives/7125">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p class="syndicated-attribution"><em>(via <a href="http://feeds.gawker.com/~r/io9/vip/~3/VzLLS_jAUQ8/the-higgs-boson-might-explain-the-origins-of-the-universe-and-dark-energy">io9</a>)</em></p>
<p><a rel="lytebox" href="http://cache.gawkerassets.com/assets/images/8/2011/09/higgsdiagram.jpg"><img src="http://cache.gawkerassets.com/assets/images/8/2011/09/500x_higgsdiagram.jpg" width="500" alt="The Higgs boson might explain the origins of the universe and dark energy" title="The Higgs boson might explain the origins of the universe and dark energy"></a>We still haven't found the Higgs boson, the hypothetical particle that explains why other particles possess mass. But that might not be the only cosmic mystery the Higgs can solve. It could also explain how the universe got its shape. </p>
<p>That's the theory put forward by researchers at Switzerland's École polytechnique fédérale de Lausanne, or EPFL. They argue that the Higgs boson might allow us to account for inflation, the otherwise unexplained process in which the early universe grew by a factor of at least 10^26 in an instant. It's not a universally accepted idea, even among physicists and cosmologists, but it seems to be the best way to account for the uniformity of the modern universe. (For an excellent, comprehensive primer on inflation, check out <a href="http://io9.com/5773158/what-really-happened-right-after-the-big-bang">this post by our own Dr. Dave Goldberg</a>.)</p>
<p>Exactly what caused inflation is still up in the air, and that's where the EPFL physicsts believe the Higgs boson enters the picture:</p>
<blockquote>
<p>In its first moments, the Universe was unimaginably dense. Under these conditions, why wouldn't gravity have slowed down its initial expansion? Here's where the Higgs boson enters the game – it can explain the speed and magnitude of the expansion, says Mikhail Shaposhnikov and his team from EPFL's Laboratory of Particle Physics and Cosmology. In this infant Universe, the Higgs, in a condensate phase, would have behaved in a very special way – and in so doing changed the laws of physics. The force of gravity would have been reduced. In this way, physicists can explain how the Universe expanded at such an incredible rate.</p>
</blockquote>
<p><a rel="lytebox" href="http://cache.gawkerassets.com/assets/images/8/2011/09/higgsdiag2.jpg"><img src="http://cache.gawker.com/assets/images/io9/2011/09/higgsdiag2.jpg" width="340" alt="The Higgs boson might explain the origins of the universe and dark energy" title="The Higgs boson might explain the origins of the universe and dark energy"></a>Here's where things get really interesting. The researchers found that, as this condensate form of the Higgs boson disappeared and the particles we know today took over, their equations permitted for the existence of a new, massless particle, which they've dubbed the dilaton. This particle is closely related to the Higgs, and shares many of its properties. But the dilaton is only similar to the Higgs - its properties happen to <em>exactly</em> describe what we observe with dark energy, the mysterious property or force that is causing the universe to accelerate its expansion.</p>
<p>The researchers had not set out to explain dark energy when they worked out what role the Higgs boson might have played in the expansion of the universe. Obviously, this is all strictly theoretical - particularly the dilaton - but the fact that their attempt to explain one cosmic mystery happens to also explain another is an encouraging sign that there may well be something to this. These are big claims, of course, and it's doesn't matter how elegant the equations are if we can't find any proof of these particles, but still...this is one hypothesis that's definitely work a closer look.</p>
<p><em>Via <a href="http://arxiv.org/abs/1107.2163">arXiv</a>. Illustrations by EPFL.</em></p><div>
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		<title>Black holes may have been fundamental building blocks of the early universe [Cosmology]</title>
		<link>http://bagofbeans.tsangal.org/archives/6032</link>
		<comments>http://bagofbeans.tsangal.org/archives/6032#comments</comments>
		<pubDate>Wed, 15 Jun 2011 20:31:53 +0000</pubDate>
		<dc:creator>author-unknown</dc:creator>
				<category><![CDATA[syndicated]]></category>
		<category><![CDATA[astrophysics]]></category>
		<category><![CDATA[black holes]]></category>
		<category><![CDATA[Breakthrough]]></category>
		<category><![CDATA[cosmology]]></category>
		<category><![CDATA[early universe]]></category>
		<category><![CDATA[science]]></category>
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		<description><![CDATA[ Most astronomers agree that at the center of every galaxy lies a supermassive black hole. But how did these gravitational monsters form? Now it seems that they may have been here since the beginning of time. 
At least, they've been here as long as the... <a href="http://bagofbeans.tsangal.org/archives/6032">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p class="syndicated-attribution"><em>(via <a href="http://feeds.gawker.com/~r/io9/vip/~3/SvsB4Tjh5jw/black-holes-may-have-been-a-fundamental-building-block-of-the-early-universe">io9</a>)</em></p>
<p><a rel="lytebox" href="http://cache.gawkerassets.com/assets/images/8/2011/06/blackholeuniverse.jpg"><img src="http://cache.gawkerassets.com/assets/images/8/2011/06/500x_blackholeuniverse.jpg" width="500" alt="Black holes may have been fundamental building blocks of the early universe" title="Black holes may have been fundamental building blocks of the early universe"></a> Most astronomers agree that at the center of every galaxy lies a supermassive black hole. But how did these gravitational monsters form? Now it seems that they may have been here since the beginning of time. </p>
<p>At least, they've been here as long as the galaxies they inhabit, which places them very near the origin of time and space as we know it.</p>
<p>Astrophysicst Ezequiel Treister and colleagues pored over hundreds of images from Chandra X-Ray Observatory, carefully tracking tiny amounts of x-ray photons originating from extremely distant (and therefore ancient) black holes at the cores of galaxies. What they discovered was that the origins of these black holes had been largely obscured by billowing clouds of gas around them as galaxies formed. But keener observation revealed that the black holes had most likely been part of these galaxies from very early in the formation of the universe — perhaps as early as a billion years after the Big Bang.</p>
<p><a rel="lytebox" href="http://cache.gawkerassets.com/assets/images/8/2011/06/figure2.jpg"><img src="http://cache.gawkerassets.com/assets/images/8/2011/06/500x_figure2.jpg" width="500" alt="Black holes may have been fundamental building blocks of the early universe" title="Black holes may have been fundamental building blocks of the early universe"></a> Treister and his collegues report in <em>Nature</em>:</p>
<blockquote>
<p>This composite image shows a small section of Chandra Deep Field South image, where the sources seen by Chandra are blue. Deep optical and infrared images from the Hubble Space Telescope are shown in green and blue and red and green respectively. Yellow circles are plotted to show the positions of very distant galaxies seen to exist when the Universe is less than about 950 million years old. The two small Chandra sources that appear on the right show all of the low and high energy X-rays that have been added up at the positions of these galaxies. This shows that growing black holes have been detected in 30% to 100% of the distant galaxies.</p>
</blockquote>
<p>(<em>Image credits: X-ray: NASA/CXC/U.Hawaii/E.Treister et al Infrared: NASA/STScI/UC Santa Cruz/G.Illingworth et al Optical: NASA/STScI/S.Beckwith et al.</em>)</p>
<p>What does this mean, exactly? It's a breakthrough in our understanding of the composition of the early universe. It means that these black holes formed the building blocks of the universe as we know it today. Black holes may be far more fundamental to our universe than we realized.</p>
<p>Harvard astrophysicist Alexey Vikhlinin assesses the new study in <em>Nature</em>:</p>
<blockquote>
<p>Treister et al. conclude that the estimated black-hole masses are consistent with a hypothesis in which the relationship between galaxy mass and blackhole mass that is observed in the local Universe is already established a billion years after the Big Bang. Treister and colleagues' results have implications for many studies of the early Universe. Unfortunately, however, answers to some key questions - such as how the progenitors of these early supermassive black holes were generated, or the exact mechanism that underlies the coevolution of the black holes and their host galaxies - will probably have to wait for the next generation of telescopes.</p>
</blockquote>
<p>You can expect more discoveries in the future, as more astrophysicists turn their attention to black holes from the early universe. Hopefully, this will help us understand exactly what our current universe is made of.</p>
<p><a href="http://www.nature.com/nature/journal/v474/n7351/full/nature10103.html">Read Treister et. al.'s full scientific article</a> via <em>Nature</em></p>
<p><em>Top illustration of the formation of the early universe via NASA/CXC/M.Weiss</em></p><div>
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		<title>The universe is at least 250 times bigger than it looks [Cosmology]</title>
		<link>http://bagofbeans.tsangal.org/archives/4010</link>
		<comments>http://bagofbeans.tsangal.org/archives/4010#comments</comments>
		<pubDate>Wed, 02 Feb 2011 00:30:49 +0000</pubDate>
		<dc:creator>author-unknown</dc:creator>
				<category><![CDATA[syndicated]]></category>
		<category><![CDATA[Astronomy]]></category>
		<category><![CDATA[astrophysics]]></category>
		<category><![CDATA[cosmology]]></category>
		<category><![CDATA[science]]></category>
		<category><![CDATA[space]]></category>
		<category><![CDATA[Universe]]></category>
		<category><![CDATA[Visible universe]]></category>

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		<description><![CDATA[The universe is so unimaginably large that parts of it are literally impossible to see, because their light is too distant to reach us even after 14 billion years. Now we might know just how big the cosmos really is. Turns out everything we can see is ... <a href="http://bagofbeans.tsangal.org/archives/4010">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p class="syndicated-attribution"><em>(via <a href="http://io9.com/#!5749332/the-universe-is-at-least-250-times-bigger-than-it-looks">io9</a>)</em></p>
<p><a rel="lytebox" href="http://cache.gawkerassets.com/assets/images/8/2011/02/6_8a4f7f5ee46b1deaa6cadfd732d2b117.jpg"><img src="http://cache.gawkerassets.com/assets/images/8/2011/02/500x_6_8a4f7f5ee46b1deaa6cadfd732d2b117.jpg" width="500" alt="The universe is at least 250 times bigger than it looks"></a>The universe is so unimaginably large that parts of it are literally impossible to see, because their light is too distant to reach us even after 14 billion years. Now we might know just how big the cosmos really is. Turns out everything we can see is less than half a percent of the entire universe.</p><p>So just how far can we see into the visible universe? Since the universe is about 14 billion years old, it seems obvious that we can only see within the nearest 14 billion light-years. But that isn't quite right, as cosmic expansion has expanded the distance between us and the most distant cosmic objects to as much as 45 billion light-years. That means that there's just about 90 billion light-years worth of visible universe that we can see.</p>
<p>But even that can't compare with the full size of the universe. Of course, if we can't see part of the universe, then we can't actually know anything about it, because no other information will have had time to reach us either. But the trick is that the structure of the universe we are able to see can reveal its overall size. Basically, the universe can have one of three structures: a closed shape like a sphere, a flat shape, or a completely open one. Either of the last two would mean the universe is infinite, but a closed spherical shape would mean the universe has a definite volume.</p>
<p>There are some subtle ways to measure the curvature of the universe. Very distant objects will be noticeably affected by the curvature of the universe - if it's closed, then the object will seem bigger than it should; if it's flat, the object will appear to be the right size; and if it's completely open, the object will look smaller than it should. A lot of different measurements have been made, but they give tons of different answers about the universe's size and curvature.</p>
<p>The trick is to combine all the conflicting data in some sort of useful way. Researchers have now used the Bayesian model, a form of statistical modeling that examines how likely given models are to be correct based on the available data. This form of modeling is far more powerful than those used before and has placed some very tight constraints on just how big the universe can be.</p>
<p>Here's what they found - in all likelihood, the universe is flat, which means it has an infinite size. But if it <em>is</em> a closed sphere, then we have a lower limit for its size, which is about 250 times the size of our visible universe. Obviously, 250 times to infinite is a pretty big range, but it's by far the tightest constraints ever put forward, and having an actual lower limit for the universe's size could prove hugely useful in other areas of cosmology.</p>
<p>For more on how the researcher came up with this, check out their <a href="http://arxiv.org/abs/1101.5476">original paper</a> or <a href="http://www.technologyreview.com/blog/arxiv/26333/">this post</a> on Technology Review.</p><div>
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		<title>Have we found the universe that existed before the Big Bang? [Cosmology]</title>
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		<pubDate>Fri, 19 Nov 2010 23:00:00 +0000</pubDate>
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		<description><![CDATA[ The current cosmological consensus is that the universe began 13.7 billion years ago with the Big Bang. But a legendary physicist says he's found the first evidence of an eternal, cyclic cosmos.The Big Bang model holds that everything that now compris... <a href="http://bagofbeans.tsangal.org/archives/2971">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p class="syndicated-attribution"><em>(via <a href="http://io9.com/5694701/does-cosmic-background-radiation-reveal-the-universe-before-the-big-bang">io9</a>)</em></p>
<p><a rel="lytebox" href="http://cache.gawkerassets.com/assets/images/8/2010/11/shutterstock_10780879.jpg"><img src="http://cache.gawkerassets.com/assets/images/8/2010/11/500x_shutterstock_10780879.jpg" width="500" alt="Have we found the universe that existed before the Big Bang?"></a> The current cosmological consensus is that the universe began 13.7 billion years ago with the Big Bang. But a legendary physicist says he's found the first evidence of an eternal, cyclic cosmos.</p><p>The Big Bang model holds that everything that now comprises the universe was once concentrated in a single point of near-infinite density. Before this singularity exploded and the universe began, there was absolutely nothing - indeed, it's not clear whether one can even use the term "before" in reference to a pre-Big-Bang cosmos, as time itself may not have existed yet. In the current model, the universe began with the Big Bang, underwent cosmic inflation for a fraction of a second, then settled into the much more gradual expansion that is still going on, and likely will end with the universe as an infinitely expanded, featureless cosmos.</p>
<p>Sir Roger Penrose, one of the most renowned physicists of the last fifty years, takes issue with this view. He points out that the universe was apparently born in a very low state of entropy, meaning a very high degree of order initially existed, and this is what made the complex matter we see all around us (and are composed of) possible in the first place. His objection is that the Big Bang model can't explain why such a low entropy state existed, and he believes he has a solution - that the universe is just one of many in a cyclical chain, with each Big Bang starting up a new universe in place of the one before.</p>
<p><a rel="lytebox" href="http://cache.gawkerassets.com/assets/images/8/2010/11/dn11172-1_640.jpg"><img src="http://cache.gawkerassets.com/assets/images/8/2010/11/500x_dn11172-1_640.jpg" width="500" alt="Have we found the universe that existed before the Big Bang?"></a></p>
<p>How does this help? Well, Penrose posits the end of each universe will involve a return to low entropy. This is because black holes suck in all the matter, energy, and information they encounter, which works to remove entropy from our universe. (Where that entropy might go is another question entirely.) The universe's continued expansion into eventual nothingness causes the black holes themselves to evaporate, which ultimately leaves the universe in a highly ordered state once again, ready to contract into another singularity and set off the next Big Bang.</p>
<p>As alternative theories go, it's not without its merits, but there's no evidence to support it...until now. He says he's found evidence for his ideas in the cosmic microwave background, the microwave radiation that permeates the universe and was thought to have formed 300,000 years after the Big Bang, providing a record of the universe at that far distant time. Penrose and his colleague Vahe Gurzadyan have discovered clear concentric circles within the data, which suggests regions of the radiation have much smaller temperature ranges than elsewhere.</p>
<p>So what does <em>that</em> mean? Penrose believes these circles are windows into the previous universe, spherical ripples left behind by the gravitational effects of colliding black holes in the previous universe. He also says these circles don't work well at all in the current inflationary model, which holds all temperature variations in the CMB should be truly random.</p>
<p>Here's where the fun begins. If the circles are really there and are really doing what Penrose says they're doing, then he's managed to overthrow the standard inflationary model. But there's a long way to go between where we are now and that point, assuming it ever happens.</p>
<p>The inflationary model has become the consensus for a good reason - it's the best explanation we've got for the universe we have now - and so cosmologists will examine any results that appear to disprove it very critically. There are also a couple key assumptions in Penrose's theory, particularly that all particles will lose their mass towards the end of the universe. Right now, we don't know whether that will actually happen - in particular, there's no proof that electrons ever decay.</p>
<p>[via <a href="http://arxiv.org/abs/1011.3706">arXiv</a>]</p>
<p><em>Shutterstock image by Kim D. French</em></p><div>
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		<title>Book: The Poincaré Conjecture</title>
		<link>http://bagofbeans.tsangal.org/archives/463</link>
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		<pubDate>Mon, 31 Mar 2008 08:24:43 +0000</pubDate>
		<dc:creator>Beanbag</dc:creator>
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		<description><![CDATA[The Poincaré Conjecture: In Search of the Shape of the Universe by Donal O&#8217;Shea. Walker &#38; Company, 2007. In The Poincaré Conjecture, Donal O&#8217;Shea explains a conjecture in topology from 1904 that had remained unsolved for nearly a century. Aside &#8230; <a href="http://bagofbeans.tsangal.org/archives/463">Continue reading <span class="meta-nav">&#8594;</span></a>]]></description>
			<content:encoded><![CDATA[<p><a href="http://www.amazon.ca/gp/product/0802716547?ie=UTF8&#038;tag=bagofbea-20&#038;linkCode=as2&#038;camp=15121&#038;creative=330641&#038;creativeASIN=0802716547"><img border="0" src="http://bagofbeans.tsangal.org/wp-content/uploads/2008/03/21qzebmbzl_aa_sl160_.jpg" style="float: right; margin:10px"></a><img src="http://www.assoc-amazon.ca/e/ir?t=bagofbea-20&#038;l=as2&#038;o=15&#038;a=0802716547" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /><br />
<em>The Poincaré Conjecture: In Search of the Shape of the Universe</em><br />
by Donal O&#8217;Shea.<br />
Walker &amp; Company, 2007.</p>
<p>In <em>The Poincaré Conjecture</em>, Donal O&#8217;Shea explains a conjecture in topology from 1904 that had remained unsolved for nearly a century.  Aside from its importance in topology, the conjecture also has implications on determining the shape of our own universe.  It is also one of the seven <a href="http://en.wikipedia.org/wiki/Millennium_Prize_Problems">Millennium Prize problems</a> listed by the Clay Institute in 2000, with a one million dollar reward for a correct solution.  It was finally solved in 2002 by Grigory Perelman and since then his solution has been accepted.  He may be eligible for the Millennium Prize but does not appear to be interested.  In 2006, he was awarded the Fields medal&mdash;the highest honor for mathematicians and which also carries a monetary reward&mdash;for his work but he declined the award.</p>
<p>In this book, O&#8217;Shea takes us through the history of the conjecture and the attempts at solving it, and also takes some time to give us the historical context along the way by describing the social and political climate surrounding each mathematician that has sought to prove the conjecture.  He does a good job of providing relatively clear and simple explanations of the complex ideas in topology and non-Euclidean geometry involved, but the book does move at a fairly brisk pace (minus the notes at the end the main text is only 200 pages long) so some work is still required to follow along, but I never felt completely lost.  This book contains a nice mix of mathematical ideas and history for a general audience, and it managed to keep my interest throughout.</p>
<p><strong>Rating:</strong> 8/10</p>
<p><strong>Links:</strong></p>
<ul>
<li><a href="http://www.amazon.ca/gp/product/0802716547?ie=UTF8&#038;tag=bagofbea-20&#038;linkCode=as2&#038;camp=15121&#038;creative=330641&#038;creativeASIN=0802716547">Amazon.ca</a><img src="http://www.assoc-amazon.ca/e/ir?t=bagofbea-20&#038;l=as2&#038;o=15&#038;a=0802716547" width="1" height="1" border="0" alt="" style="border:none !important; margin:0px !important;" /></li>
<li><a href="http://www.librarything.com/work/2510042/book/28478547">LibraryThing</a></li>
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<p><strong>Related:</strong></p>
<ul>
<li><a href="http://bagofbeans.tsangal.org/archives/438">Book: The Möbius Strip</a></li>
</ul>
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